The scores of the match were 25-15, 21-25, 26-24 and 25-19.
The Bulldogs improved to 9-0 in conference and 13-5 overall to maintain a two-game lead in the Ivy League standings. Columbia fell to 4-5 in Ivy play and 9-9 overall.
Johnson had a team-high 13 kills with 11 digs and 17 assists, while Haley Wessels hit .524 with 12 kills and Mollie Rogers (12 kills) and Erica Reetz (10 kills) reached double figures in kills to help Yale win its 10th match in a row.
After dominating the first set, the Bulldogs were outplayed most of the second. Yale then fell behind in the third and needed a lift.
With the match tied at one set apiece, Columbia took a 22-18 lead in the third set after a kill from Megan Gaughn. Yale scored the next four points, capitalizing on two Lions' errors and kills from Johnson and Wessels.
After a kill from Denise Dearman, Columbia regained the lead. Rogers responded with a kill and Columbia gave Yale its first lead of the set.
Gaughn, who tallied a match-high 22 kills, tied the set one more time before Johnson put Yale back in front. Rudnick fired a low, line drive ace to end the set.
Reetz provided three kills in a 4-0 run to start the fourth. Yale bolted out to a 13-6 lead - a run capped by a kill from Johnson. The Bulldogs never trailed in the fourth set.
Rogers served up eight straight points to begin the match as the the Bulldogs led the entire first set. Columbia used a run midway through the second to top Yale in the set.
The Bulldogs go for 11 straight wins against Cornell on Saturday at 5 p.m. in New Haven.
Report filed by Ernie Bertothy, Yale Sports Publicity